TY - JOUR

T1 - Delaunay triangulation structured kriging for surface interpolation

AU - Felus, Yaron A.

AU - Saalfeld, Alan

AU - Schaffrin, Burkhard

PY - 2005/3

Y1 - 2005/3

N2 - Surface interpolation is an essential tool in surveying and geographical information systems projects. For example, given a list of observations (e.g. elevations, gravity or magnetic field values, and underground-water levels), a prediction of a value at an unobserved location is made. Surveyors and engineers commonly use Triangulated Irregular Network (TIN) based linear interpolation for surface interpolation. TIN interpolation is computationally very efficient, utilizing a Delaunay triangulation algorithm and simple mathematical function. However, the TIN method uses only three local data points. Therefore, it is often less accurate and will yield a higher Mean Square Prediction Error (MSPE). Kriging is a relatively new, accurate interpolation method which yields a smaller Mean Square Prediction Error (MSPE). Nevertheless, kriging is computationally inefficient and requires the inversion of an nxn matrix where n is the number of data points. A unique approach is presented here that combines these two techniques such that the Delaunay triangulation data-structure is used to determine the interpolation neighborhood of a kriging prediction process. The new TIN-based kriging algorithm is used to interpolate aeromagnetic data for a geographical information system developed in West Antarctica. A comparison is made between global kriging, TIN linear interpolation, and the TIN-structured kriging.

AB - Surface interpolation is an essential tool in surveying and geographical information systems projects. For example, given a list of observations (e.g. elevations, gravity or magnetic field values, and underground-water levels), a prediction of a value at an unobserved location is made. Surveyors and engineers commonly use Triangulated Irregular Network (TIN) based linear interpolation for surface interpolation. TIN interpolation is computationally very efficient, utilizing a Delaunay triangulation algorithm and simple mathematical function. However, the TIN method uses only three local data points. Therefore, it is often less accurate and will yield a higher Mean Square Prediction Error (MSPE). Kriging is a relatively new, accurate interpolation method which yields a smaller Mean Square Prediction Error (MSPE). Nevertheless, kriging is computationally inefficient and requires the inversion of an nxn matrix where n is the number of data points. A unique approach is presented here that combines these two techniques such that the Delaunay triangulation data-structure is used to determine the interpolation neighborhood of a kriging prediction process. The new TIN-based kriging algorithm is used to interpolate aeromagnetic data for a geographical information system developed in West Antarctica. A comparison is made between global kriging, TIN linear interpolation, and the TIN-structured kriging.

KW - Aeromagnetic data

KW - Delaunay triangulation

KW - Interpolation

KW - Kriging

UR - http://www.scopus.com/inward/record.url?scp=20444494286&partnerID=8YFLogxK

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AN - SCOPUS:20444494286

SN - 1538-1242

VL - 65

SP - 27

EP - 36

JO - Surveying and Land Information Science

JF - Surveying and Land Information Science

IS - 1

ER -